Question

Find the vertical asymptotes, if any, of the graph of the rational function. Show your work. x/x^2+1

Answers are in the picture please help

Answer 1

Answer: Choice C) no vertical asymptote

Set the denominator x^2+1 equal to zero and solve for x
x^2+1 = 0
x^2 = -1
x = sqrt(-1) or x = -sqrt(-1)
x = i or x = -i
The two results (i and -i) are nonreal values

There are no real numbers we can plug into x^2+1 to get to 0
The smallest x^2+1 can get is 1
Because its not possible to have x^2+1 be zero (if x is real) this means we don't run into dividing by zero errors. This is why there are no vertical asymptotes.